The efficiency can be improved however if we move only one electron at the time. The Slater determinant matrix \( \hat{D} \) is defined by the matrix elements

$$ d_{ij}=\phi_j(x_i) $$

where \( \phi_j(\mathbf{r}_i) \) is a single particle wave function. The columns correspond to the position of a given particle while the rows stand for the various quantum numbers.